Theoretical analysis.
We provide a theoretical analysis to reveal
the connection between GMPT-CL with approximate contrastive training and mutual information maximization.
Firstly, we show that,

Minimizing Eqn. (REF ) is equivalent to
maximizing a lower bound of the mutual information
between the latent representations of two views of graphs.

Furthermore, we show that,

Optimizing Eqn. (REF ) with approximate contrastive training algorithm has the same optimization lower bound as originally in expectation.

Thus we can see that the proposed approximate contrastive training
fits the formulation of the InfoNCE loss [1]}, [2]} in expectation.
The proofs are provided in Supplementary Material S.3.
